ANALYTIC CAPACITY - DISCRETE APPROACH AND CURVATURE OF MEASURE

Certain discrete 'computable' quantities are introduced, and their interconnections and relations with analytic capacity are found out. The concept of curvature of a measure is introduced, which emerges naturally in the computations of the L(2)-norm of the Cauchy transform of this measure. A. lower bound on the analytic capacity, which uses the measure curvature and which has, to this extent, a geometric nature, is obtained.